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A027066 a(n) = A027052(n, 2n-10).

%I A027066 #11 Nov 07 2019 08:28:12
%S A027066 1,1,3,11,37,125,423,1429,4811,16111,53589,176905,579407,1882943,
%T A027066 6073469,19452705,61900375,195799527,615978629,1928297807,6009527345,
%U A027066 18653079889,57686469763,177812890843,546456642501,1674844848629
%N A027066 a(n) = A027052(n, 2n-10).
%H A027066 G. C. Greubel, <a href="/A027066/b027066.txt">Table of n, a(n) for n = 5..750</a>
%p A027066 T:= proc(n, k) option remember;
%p A027066       if k<0 or k>2*n then 0
%p A027066     elif k=0 or k=2 or k=2*n then 1
%p A027066     elif k=1 then 0
%p A027066     else add(T(n-1, k-j), j=1..3)
%p A027066       fi
%p A027066     end:
%p A027066 seq( T(n,2*n-10), n=5..30); # _G. C. Greubel_, Nov 06 2019
%t A027066 T[n_, k_]:= T[n, k]= If[k<0 || k>2*n, 0, If[k==0 || k==2 || k==2*n, 1, If[k==1, 0, Sum[T[n-1, k-j], {j, 3}]]]]; Table[T[n,2*n-10], {n,5,30}] (* _G. C. Greubel_, Nov 06 2019 *)
%o A027066 (Sage)
%o A027066 @CachedFunction
%o A027066 def T(n, k):
%o A027066     if (k<0 or k>2*n): return 0
%o A027066     elif (k==0 or k==2 or k==2*n): return 1
%o A027066     elif (k==1): return 0
%o A027066     else: return sum(T(n-1, k-j) for j in (1..3))
%o A027066 [T(n,2*n-10) for n in (5..30)] # _G. C. Greubel_, Nov 06 2019
%K A027066 nonn
%O A027066 5,3
%A A027066 _Clark Kimberling_